Random sampling of random processes: Stationary point processes

Random Sampling of Random Processes: Stationary Point Processes

This is the first of a series of papers treating randomly sampled random processes. Spectral analysis of the resulting samples presupposes knowledge of the statistics of 1 t~}, the random point process whose variates represent the sampling times. We introduce a class of s ta t ionary point processes, whose s ta t ionar i ty (as characterized by any of several equivalent criteria) leads to wide-...

Random sampling of long-memory stationary processes

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the e...

Memory-Universal Prediction of Stationary Random Processes

We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process fXig1i= 1. The best mean-square predictor of X0 is its conditional mean given the entire infinite past fXig 1 i= 1. Given a sequence of observations X1 X2 XN , we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasi...

Random Functions and Point Processes

Spectral decomposition of locally stationary random processes

The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station­ ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...